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3 years ago

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Mathematics

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SIZIF [17.4K]3 years ago

7 0

Answer:

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Expand (2x+2)^6 How would you find the answer using the binomial theorem?

Yanka [14]

Answer:

Step-by-step explanation:

$\displaystyle\\\sum\limits _{k=0}^n\frac{n!}{k!*(n-k)!}a^{n-k}b^k .\\\\k=0\\\frac{n!}{0!*(n-0)!}a^{n-0}b^0=C_n^0a^n*1=C_n^0a^n.\\\\ k=1\\\frac{n!}{1!*(n-1)!} a^{n-1}b^1=C_n^1a^{n-1}b^1.\\\\k=2\\\frac{n!}{2!*(n-2)!} a^{n-2}b^2=C_n^2a^{n-2}b^2.\\\\k=n\\\frac{n!}{n!*(n-n)!} a^{n-n}b^n=C_n^na^0b^n=C_n^nb^n.\\\\C_n^0a^n+C_n^1a^{n-1}b^1+C_n^2a^{n-2}b^2+...+C_n^nb^n=(a+b)^n.$

$\displaystyle\\(2x+2)^6=\frac{6!}{(6-0)!*0!} (2x)^62^0+\frac{6!}{(6-1)!*1!} (2x)^{6-1}2^1+\frac{6!}{(6-2)!*2!}(2x)^{6-2}2^2+\\\\ +\frac{6!}{(6-3)!*3!} (2a)^{6-3}2^3+\frac{6!}{(6-4)*4!} (2x)^{6-4}b^4+\frac{6!}{(6-5)!*5!}(2x)^{6-5} b^5+\frac{6!}{(6-6)!*6!}(2x)^{6-6}b^6. \\\\$

$(2x+2)^6=\frac{6!}{6!*1} 2^6*x^6*1+\frac{5!*6}{5!*1}2^5*x^5*2+\\\\+\frac{4!*5*6}{4!*1*2}2^4*x^4*2^2+ \frac{3!*4*5*6}{3!*1*2*3} 2^3*x^3*2^3+\frac{4!*5*6}{2!*4!}2^2*x^2*2^4+\\\\+\frac{5!*6}{1!*5!} 2^1*x^1*2^5+\frac{6!}{0!*6!} x^02^6\\\\(2x+2)^6=64x^6+384x^5+960x^4+1280x^3+960x^2+384x+64.$

8 0

1 year ago

A rental car company charges $31.91 per day to rent a car and $0.07 for every mile driven. Hudson wants to rent a car, knowing t

qaws [65]

The inequality that can be used to determine x is $31.91x + 7 \leq 70$

<h3>How to generate the inequality</h3>

Given data

Rental company charge per day = $31.91

Rental company charge per mile driven = $0.07

Hudson plans to drive 100 miles

Hudson has at most $70

solution

let x represent he maximum number of days Hudson can afford to rent while staying on budget. cost of number of days is:

$31.91 * x= 31.91x

As Hudson plans to ride 100 miles; cost is:

100 * 0.07 = $7

therefore number of days plus 100 miles ride is:

31.91x + 7

with a limit of less than or equal to the budget we have:

$31.91x + 7 \leq 70$

The inequality above could be used to determine x

Read more on inequality here: brainly.com/question/11613554

#SPJ1

6 0

1 year ago

13. A cone with a radius of 3 inches and a height of 7 inches has the same radius as a cylinder. If the cylinder's volume is two

Ghella [55]

Answer:

Step-by-step explanation:

r = 3 in

h = 7 in

volume of cone = ⅓πr²h = 21π in³

cylinder has radius r = 3 and height h.

volume of cylinder = πr²h = 9πh in³

volume of cylinder is two times the volume of cone

9πh = 2×21π

9h = 42

h = 42/9 = 4⅔ in

3 0

3 years ago

What value of x is in the solution set of 4x – 12 < 16 + 8x? -10 -9 -8 -7

Akimi4 [234]

Answer:

Step-by-step explanation:

4x - 12 ≤ 16 + 8x

4x - 8x ≤ 16 + 12

- 4x ≤ 28

x ≥ - 7 or [ - 7, ∞ )

3 0

3 years ago

Someone Plz help ASAP!!!

Butoxors [25]

Answer:

c=3/16

n=4/3

Step-by-step explanation:

6 0

3 years ago